Fractional Diffusion–Wave Equation with Application in Electrodynamics

Fractional Diffusion–Wave Equation with Application in Electrodynamics

We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity. For this equation, we solve an asympotic boundary value problem without initial conditions, construct a representation of i...

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Bibliographic Details
Main Authors: Arsen Pskhu, Sergo Rekhviashvili
Format: Article
Language:English
Published: MDPI AG 2020-11-01
Series:Mathematics
Subjects:
diffusion–wave equation
fundamental solution
fractional derivative on infinite interval
asympotic boundary value problem
problem without initial conditions
Gerasimov–Caputo fractional derivative
Online Access:https://www.mdpi.com/2227-7390/8/11/2086
Description
Summary:We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity. For this equation, we solve an asympotic boundary value problem without initial conditions, construct a representation of its solution, find out sufficient conditions providing solvability and solution uniqueness, and give some applications in fractional electrodynamics.
ISSN:2227-7390

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